Lloth specifically blesses her followers with red eyes to mark them as 'hers'.
No, she doesn't. That's the problem.
To quote the character creator in Baldur's Gate III: "Loth marks her followers with bright red eyes so the Underdark will learn to fear drow on sight."
The red/purple eyes in BG III is an invention on the part of Larian that contradicts established lore spanning 5 editions of D&D and multiple decades. Pointing out that Larian wrote that into BG III doesn't prove anything, because wee are very much aware of that blurb-it's the precise target of the criticism here.
There's also a post directly above yours with multiple examples of Lolth-worshipping drow who weren't marked with red eyes. with pictures, if that would help.